Solve each optimization problem. 1) A supermarket employee wants to construct an open-top box from a 14 by 30 in piece of cardboard. To do this, the employee plans to cut out squares of equal size from the four comers so the four sides can be bent upwards. What size should the squares be in order to create a box with the largest possible volume? 2) A cryptography expert is deciphering a computer code. To do this, the expert needs to minimize the product of a positive rational number and a negative rational number, given that the positive number is exactly 8 greater than the negative number. What nal product is the expert looking for? 3) A farmer wants to construct a rectangular pigpen using 300 ft of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area